2. Determine whether the function f(x) is a valid probability distribution (PMF) for a random variable...
Please answer the question clearly
1. Find the probability distribution (PMF) of Y, denoted by f(y), where Y is the absolute differ- ence between the number of heads and the number of tails obtained in four tosses of a balanced coin 2. Determine whether the function f(x) is a valid probability distribution (PMF) for a random variable with the range r - 0,1,2,3, 4. r2 f()30 3. Suppose X is a random variable with probability distribution (PMF) given by f(x)...
he cumulative distribution function (cdf), F(z), of a discrete ran- om variable X with pmf f(x) is defined by F(x) P(X < x). Example: Suppose the random variable X has the following probability distribution: 123 45 fx 0.3 0.15 0.05 0.2 0.3 Find the cdf for this random variable
A probability distribution function for a random variable X has the form Fx(x) = A{1 - exp[-(x - 1)]}, 1<x< 10, -00<x<1 (a) For what value of A is this a valid probability distribution function? (b) Find the probability density function and sketch it. (c) Use the density function to find the probability that the random variable is in the range 2 < X <3. Check your answer using the distribution function. (d) Find the probability that the random variable...
1. 20 points Let X be a random variable with the following probability density function: f(x)--e+1" with ? > 0, ? > 0, constants x > ?, (a) 5 points Find the value of constant c that makes f(x) a valid probability mass function. (b) 5 points Find the cumulative distribution function (CDF) of X.
2. Suppose X is a continuous random variable with the probability density function (i.e., pdf) given by f(x) - 3x2; 0< x < 1, - 0; otherwise Find the cumulative distribution function (i.e., cdf) of Y = X3 first and then use it to find the pdf of Y, E(Y) and V(Y)
Suppose that the probability mass function for a discrete random variable X is given by p(x) = c x, x = 1, 2, ... , 6. Find the value of the cdf F(x) for 3 ≤ x < 4.
Find the density function of Y2x+8 9. Let R have probability mass function (pmf) pr)-1/8 for r1,8 Find (I)the cumulative distribution function (cdf) of R; (2)P(R>5): (S)EI(R-3)(R-)) (6)Var(R 10 Suppose the density function of a random variable X is f(x)sige 2- x > 0, where σ>0 is constant. Find E(X) and D()
C2.1 (Probability integral transform.) Let X be a random variable with cu mulative distribution function F, and suppose that F is continuous and strictly increasing on R. (i) Show that F has a well-defined inverse function G : (0,1) → R, which is (ii) Using G, or otherwise, show that the random variable F(X) is uniformly 시 strictly increasing distributed on [0,1
Suppose that X is a random variable whose cumulative distribution function (cdf) is given by: F(x) = Cx -x^2, 0<x<1 for some constant C a. What is the value of C? b. Find P(1/3 < X < 2/3) c. Find the median of X. d. What is the expected value of X?
2-2.3 A probability distribution function for a random variable has the form F,(x) = A(1-exp[-(x-1)) 1 < x < oo -00<xs1 a) For what value of A is this a valid probability distribution function? b) What is Fx (2)? c) What is the probability that the random variable lies in the interval 2 X < 00? d) What is the probability that the random variable lies in the interval 1 <X s3?